In a device of the above type known from DE-PS 29 09 803, the problem arises on starting of the internal combustion engine that the adjusting piston moves at a high speed into a position of maximum displacement in which its repeated abutting is accompanied by a considerable amount of noise. This is due to the fact that when the engine has been turned off, the hydraulic medium contained in the device gradually escapes therefrom so that the adjusting piston is no longer sufficiently supported hydraulically. Due to the torsional vibrations of the camshaft, the adjusting piston, because of a lack of hydraulic support, is displaced into an end. position on re-starting of the engine, with the already mentioned, considerable noise generation. This state prevails during the period of time between the ignition of the engine and the filling of the pressure chambers, that is to say, for a few seconds after the engine has been started.